Non technical explanation. Hoping this helps...
Example 1: A single host VPN for a business goes from point A (your home for example) to point B (work). A tunnel is created and traffic is usually encrypted. But, the IP information of where your traffic is coming from (your home) and where it's going to (your work) is not encrypted or hidden. Otherwise routers along the way wouldn't know what to do unless they had the decrypt keys or algorithms. So, traffic is encrypted but no anonymity at that point. If the traffic at your office was traced it'd be from your house.
Example 2: You have a single host VPN on your laptop and you connect from point A (home) to a point B (3rd party company that you are paying for your VPN). At this point there's no anonymity for you yet. The traffic is encrypted though. Then, you go to a web page and it goes to point B, which has the ability to decrypt the traffic) . Point B then "re-writes" the web page request and routes it to other servers (proxies) before sending it to your desired web page. Some VPN companies can make your traffic go to a diffrent country before going to the web page. That's where anonymity comes from. If the company that owns the website tracks the traffic it will look like it only came from the company you are paying for the VPN (or the proxies they used). You are trusting the company you purchase your VPN from to keep your connections private. That's your anonymity.
This is a "layman's" way to explain this. Please understand, technically it's more complex but this should help the basic understanding.